You report to a Polling station, it depends on where you live, the zone. You enter and report to the poll worker at the desk. You give your name and sometimes a ID, she/he crosses your name out of a print out sheet with a ruler and pen. She hands you a ballot, there are a number of boxes with curtains, you enter a box and draw the curtain. You then select who you want or leave the name blank or fill in your own whoever. You exit the box and place the ballot in a 'ballot box' which adds another number to the amount of ballots already in the box from previous voters. You leave. Very easy.
First you must be a registered voter. This can be done at your local county courthouse. Then on Election Day show up at the designated polling office and cast your ballot. If you know you're not going to be available to vote on Election Day, you can apply to vote absentee. Many places also offer early voting.